Center for Financial Innovation and Stability

Notes from the Vault
Urban Jermann, Bin Wei, and Vivian Yue
September 2018

The foreign exchange rate is the rate at which one currency can be exchanged for another and, as such, it is an important determinant of the price of imports and exports. As China is one of the world's largest importers and exporters, the exchange rate for its currency, the renminbi or RMB, is not only important to the Chinese but also to the global economy. Additionally, the RMB exchange rate and especially trends in that rate can have important consequences for capital flows (the movement of money between countries), which is an especially important consideration for the financial system of developing countries such as China.¹

There are a wide variety of exchange rate policies a country can follow. At one extreme, the currency can be allowed to float, with its value being set in foreign exchange markets. At the other extreme, the exchange can be fixed with regard to some other asset or bundle of assets (typically, some other foreign currency).² On July 21, 2005, China depegged its currency from the U.S. dollar and followed a "managed floating" exchange rate policy that allows the RMB to move toward its market rate but at a controlled pace. However, exactly how China implemented the exchange rate policy in practice was unclear. In this Notes from the Vault post, we summarize our recent working paper on how China managed its currency from December 2015 to May 2017.

Recent managed floating exchange rate system in China
In the current managed floating regime, every morning the People's Bank of China (PBC) announces the "central parity rate" (also known as the midpoint price) and permits the RMB/U.S. dollar (USD) exchange rate to fluctuate within a band around the central parity rate. Currently, the width of the band is officially 2 percent on either side. Effectively, though, that width has recently been limited to 0.5 percent. To make the RMB more "market determined," the PBC reformed the formation mechanism of the central parity rate on August 11, 2015, such that the midpoint would be primarily based on the previous day's closing rate in the spot market. Due to possible rate hikes by the Federal Reserve and the slowing Chinese economy, the RMB was subsequently expected to depreciate. To mitigate depreciation expectations, the PBC modified the policy on December 11, 2015, and introduced three trade-weighted RMB baskets or indices known as CFETS (China Foreign Exchange Trade System), BIS (Bank for International Settlements), and SDR (International Monetary Fund's Special Drawing Rights).³ As stated in the 2016 first-quarter "China Monetary Policy Report," under the modified policy, "market makers must consider both factors when quoting the central parity of the RMB to the USD, namely the 'previous closing rate' and the 'changes in the currency basket'."⁴

Several studies of the managed floating regime prior to 2015 focused on uncovering the unknown weights of the currencies in the PBC's currency basket (see, for instance, Frankel [2009]). Our own recent work (Jermann, Wei, and Yue, 2017) focused on formalizing the PBC's modified approach since the end of 2015. We label this modified approach the "two-pillar policy": one pillar refers to the "previous closing rate" that "reflects the market demand and supply situation," while the other refers to "changes in the currency basket" that "maintain the overall stability of the RMB to the currency basket."

In our recent work, we provide empirical evidence that the two-pillar policy we formulated provides a good description of the recent exchange rate policy in China, especially in the period between December 2015 and May 2017. More importantly, we develop a theoretical framework to analyze the two-pillar policy further. Our theoretical framework allows us to estimate the probability of continuation of the two-pillar approach using derivatives data. The change of a country's exchange rate regime can have dramatic effects on the value of the currency and large impacts on the global economy in the case of China.⁵ Our work provides helpful real-time estimates of a possible change in China's exchange rate policy.

The two-pillar policy: formulation
Our starting point for analyzing the Chinese managed floating rate system is determining how the PBC determined the central parity rate for the USD, the midpoint of its daily trading range for the RMB versus the USD. The PBC's statements make it clear this rate depends on the two pillars of yesterday's closing rate and the rate that would be expected based on changes in (one of) the currency baskets. As explained in the 2016 first-quarter "China Monetary Policy Report," the former reflects the "market demand and supply situation," while the latter is referred to as "the amount of the adjustment in the exchange rate of the RMB to the USD, as a means to maintain the overall stability of the RMB to the currency basket." However, these statements do not explain exactly how the PBC calculates the central parity rate.

The first problem is obtaining the values for each of the two pillars. The first pillar, yesterday's closing exchange rate between the RMB and USD, is readily observable but the change due to the basket is not. According to the 2016 first-quarter "China Monetary Policy Report," this second pillar is defined so as to keep the RMB index unchanged from the previous day. It turns out the second pillar is closely related to the well-known U.S. dollar index that is actively traded on financial markets, DXY. The key idea is that movements in the RMB index are attributable to movements in either the value of the RMB relative to the U.S. dollar, the value of the dollar relative to the basket of nondollar currencies in the RMB index, or both. The relative contributions of these two types of movements are determined by w_USD and 1 – w_USD, respectively, with w_USD being the dollar's weight in the RMB index. As shown in our working paper, we construct the latter basket of nondollar currencies for each of the three RMB indices and find that regardless of the RMB index used in construction, the nondollar basket is highly correlated with the existing U.S. dollar index, DXY. As a result, in order for the RMB index to remain unchanged in response to movement in the U.S. dollar index, hypothetically, the value of the RMB relative to the USD should be at a level that exactly offsets such movement. In mathematical terms this takes the form of

where w_USD is the dollar's weight in the RMB index and DXY_t represents the dollar basket of the non-RMB currencies implied by the RMB index that is highly correlated with the U.S. dollar index with ticker DXY. The China Foreign Exchange Trade System started publishing three RMB indices on December 11, 2015, and disclosed the corresponding weights. We estimate our model separately for each of the three indices because the PBC has not officially stated which index it uses.

Given values for each of the two pillars, the next problem is to determine how the two pillars are weighted. We assume the PBC uses a geometrically weighted average of the two rates and use our model to estimate these weights. In mathematical terms, this takes the form:

where is the central parity rate at day t+1, is the rate that achieves the "stability" of the RMB index, and is day t's close. and are the two pillars of the central parity. Intuitively, the two-pillar policy allows the PBC to make the RMB flexible and more market driven through the second pillar,, and at the same time keep it stable relative to the RMB index through the first pillar, . At one extreme, when weight w is fixed at 100 percent, the central parity is fully determined by the first pillar; that is, the exchange rate policy is essentially basket pegging and the RMB index does not change over time. At the other extreme, when weight w is fixed at zero, the central parity is fully determined by the second pillar and is thus market driven to the extent that the spot exchange rate is permitted to fluctuate within a band around the central parity rate under possible interventions by the PBC.

Empirical findings
To estimate empirically the weighting scheme, we convert the previous equation into logs and estimate the weights in a regression equation. Specifically, we regress the one-day percentage change of the central parity rate on its two pillars normalized by the previous central parity rate. The regression coefficients are thus associated with the weights put on the two pillars.

Our regression results suggest the weights on both pillars are roughly equal in the period between December 2015 and May 2017. The exact choice of the basket does not seem to matter much. Furthermore, our two-pillar framework has a great explanatory power, with our regression results suggesting that about 80 percent of the dynamics of the central parity rate can be explained by the two pillars within our framework. These results suggest a tight adherence to our formulation of the two-pillar policy.

To detect possible time variations in the weighting scheme, we also conducted 60-day rolling-window regressions of the same equation. Chart 1 plots the regression coefficient α, which corresponds to the weight w. As shown in chart 1, the weighting scheme has gradually settled toward equal weighting in May 2016.

Theoretical model and estimation results
For the period between December 11, 2015, and May 23, 2017, the two-pillar policy—combined with an effective 0.5 percent trading band—restricted the exchange rate dynamics. Expectations about further RMB depreciations and a possible change in policy have also affected exchange rates during that time. Specifically, in a no-arbitrage environment, changes to the future value of the RMB (for instance, as a result of a possible change in policy) would lead to changes in current demand for the RMB and thus affect its current value. We built a no-arbitrage model to quantify these expectations.

We combine the documented properties of the two-pillar policy with the tractable no-arbitrage model from Jermann (2017). The theoretical model captures several important features of the exchange rate regime. Specifically, we can model the extent to which it aligns the value of the RMB with its fundamental or so-called equilibrium value and the likelihood perceived by market participants the regime will remain unchanged. More importantly, we estimate the model using derivatives data to quantify the aforementioned measures. In our estimation, we use options and futures data for both the RMB and the U.S. dollar index. The forward-looking nature of these derivatives makes them informative about the unobserved equilibrium value of the RMB and the likelihood of the current policy to persist.

The model is parsimonious and allows for an occasionally binding band around the central parity. In the model, we assume the two-pillar policy may or may not continue in the future. In the latter case, it would be replaced by an alternative policy with an exchange rate we label the "fundamental exchange rate," which can be considered as the rate that would prevail if the current policy is abandoned.

Fitting the model to data of the spot rate and RMB option prices, we estimate the fundamental exchange rate and the continuation probability of the two-pillar policy (see chart 2). The model is estimated for the period between December 11, 2015, and May 23, 2017. We choose December 11, 2015, because it is the starting date of the two-pillar policy following the introduction of the RMB indices on that date. We choose May 23, 2017, as the end date of the sample because our model implies an essentially zero probability the two-pillar policy would continue in the near future. This is consistent with the PBC's statement on May 26, 2017, confirming it had recently changed its policy and added a "countercyclical factor" to the formation mechanism of the central parity.⁶

We find that during the sample period, the RMB has been valued on average about 3 percent higher than its fundamental value, which is consistent with recent expectations of further depreciation of the RMB. The two-pillar policy had mostly high credibility over the sample. During May 2017, the probability dropped from about 80 percent to close to zero, as the model correctly forecasts that the end of the two-pillar policy was approaching. Our results suggest the PBC seems to have stopped following the two-pillar regime in May 2017.

Conclusion
The foreign exchange rate for China's RMB is important for both global markets and China's financial system, with that rate being determined by a managed float. The PBC has provided a general explanation for how it manages the value of the RMB, but the underlying mechanism still remains opaque. This post summarizes our recent working paper that provides a good explanation of how that procedure has worked in the past. More importantly, we develop the first possible quantitative model of China's recent exchange rate policy that can be estimated using market data to provide market participants' view about several key aspects of the policy, such as the fundamental value of the RMB and credibility of the policy.

References

Frankel, Jeffrey, 2009, "New Estimation of China's Exchange Rate Regime." Pacific Economic Review 14, 346–360.

Frankel, Jeffrey, and Shang-Jin Wei, 2007, "Assessing China's Exchange Rate Regime." Economic Policy 22, 576–627.

Jahjah, Samir, Bin Wei, Vivian Yue, 2013, "Exchange Rate Policy and Sovereign Bond Spreads in Developing Countries." Journal of Money, Credit and Banking 45, 1275–1300.

Jermann, Urban, 2017, "Financial Markets' Views about the Euro-Swiss Franc Floor." Journal of Money, Credit and Banking 49, 553–565.

Jermann, Urban, Bin Wei, and Vivian Yue, 2017, "The Two-Pillar Policy for the RMB." Unpublished manuscript.

Levy-Yeyati, Eduardo, and Federico Sturzenegger, 2003, "To Float or to Fix: Evidence on the Impact of Exchange Rate Regimes on Growth." American Economic Review 93, 1173–93.

People's Bank of China, 2016 first-quarter "China Monetary Policy Report."

Urban Jermann is Safra Professor of International Finance and Capital Markets at the Wharton School at the University of Pennsylvania, Bin Wei is a financial economist and associate policy adviser at the Atlanta Fed, and Vivian Yue is associate professor of economics at Emory University and a senior research fellow in the Center for Quantitative Economic Research at the Atlanta Fed. The authors thanks Larry Wall for helpful comments. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. If you wish to comment on this post, please email Bin Wei at bin.wei@atl.frb.org or Vivian Yue at vyue@emory.edu or send an email to atl.nftv.mailbox@atl.frb.org.

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¹ See, for example, Frankel and Wei (2007) and Frankel (2009) for more discussion on related issues.

² The United States has been allowing the value of the U.S. dollar to be determined by markets, according to the Federal Reserve Board.

³ In a trade-weighted RMB basket, China uses the extent to which it trades goods and services with each country to determine the weights on individual currencies in the basket. Specifically, the CFETS index mainly refers to the CFETS (China Foreign Exchange Trade System) currency basket whose currency weight is calculated by international trade weight with adjustments of re-export trade factors. The weighting scheme in the BIS or SDR indices is based on the weights in the Bank for International Settlements (BIS) or the International Monetary Fund’s Special Drawing Rights (SDR) basket.

⁴ See the PBC 2016 first-quarter "China Monetary Policy Report."

⁵ Countries change exchange rate regimes for a variety of reasons. See, for example, Levy-Yeyati and Sturzenegger (2003) and Jahjah, Wei, and Yue (2013) as well the references therein for more detail. In the case of China, there is a significant chance of the RMB regime moving in a direction closer to a fixed peg or a free float.

⁶ See the statement on the CFETS website: http://www.chinamoney.com.cn/english/.